Question

A natural number x is chosen at random from the first 100 natural numbers. Then the probability that, $x+\frac{100}{x}>50$ is:

• A. $\frac{1}{20}$
• B. $\frac{11}{20}$
• C. $\frac{1}{3}$
• D. $None$

Answer 1

The correct option is B $\frac{11}{20}$

$x+\frac{100}{x}>50\Rightarrow x^2-50x+100>0,1\le x\le 100,x\in Z.$
$\Rightarrow 1\le x<25-5\sqrt{21}$ or $25+5\sqrt{21}<x\le 100$
$\Rightarrow x=1,2,48,49,......,100.$
$\therefore$ Total number of ways = 100,
and favourable ways = 55..
$\therefore$ Required probability =$\frac{55}{100}=\frac{11}{20}$